Self-diffusion and viscoelasticity of linear polystyrene in entangled solutions

Nemoto, Norio; Kishine, Masahiro; Inoue, Tadashi; Osaki, Kunihiro

doi:10.1021/ma00007a030

Cited by 38 publications

(70 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The PMC approach naturally includes the constraint porosity effects as it starts from the microscopic correlations of the polymeric liquid structure. This is especially necessary in polymer solutions where the density screening length is not small compared to the entanglement length; δ ) F /b ) 0.3 is found for the PS solution data of Nemoto et al [26][27][28] This length scale ratio is larger in solutions than in melts, as has been argued in section 2. It is rather intriguing, but not understood at present, that the ratios of the asymptotic prefactor, λ D , in solution to the one in melts and of the length scale δ in solution to its value in melts, are rather similar:…”

Section: Rmentioning

confidence: 82%

“…Except for PMC theory, where the tracer shape fluctuations are found responsible, no other consistent theoretical explanation apparently exists for these anomalously shallow high-frequency wings of the dielectric and shear moduli spectra. The measurements of tracer diffusion constants in immobile polymer solutions, i.e., in matrices of high molecular weight polymers [26][27][28][29] , and in gels 74,75 indicate that strong deviations from reptation-like asymptotes can exist even if constraint release corrections are absent. The observation of a D ∼ M -2.5 scaling in semidilute and concentrated solutions, [26][27][28] and of D ∼ M -2 in melts, 66,77 appears to require a proper theoretical treatment of the polymer liquid structure.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Fuchs

Schweizer

1997

Macromolecules

View full text Add to dashboard Cite

The predictions of polymer mode coupling theory for the finite size corrections to the transport coefficients of entangled polymeric systems are tested in comparison with various experimental data. It is found that quantitative descriptions of the viscosities, η, dielectric relaxation time, τ , and diffusion coefficients, D, of polymer melts can be achieved with two microscopic structural fit parameters whose values are in the range expected from independent theoretical or experimental information. An explanation for the (apparent) power law behaviors of η, τ , and D in (chemically distinct) melts for intermediate molecular weights as arising from finite size corrections, mainly the self-consistent constraint release mechanism, is given. The variation of tracer dielectric relaxation times from Rouse to reptationlike behavior upon changes of the matrix molecular weight is analyzed. Self-diffusion and tracer diffusion constants of entangled polymer solutions can be explained as well, if one further parameter of the theory is adjusted. The anomalous scaling of the tracer diffusion coefficients in semidilute and concentrated polystyrene solutions, D ∼ N -2.5 , is predicted to arise due to the spatial correlations of the entanglement constraints, termed "constraint porosity". Extensions of the theory to polymer tracer diffusion through poly(vinyl methyl ether) and polyacrylamide gels provide an explanation of the observation of anomalously high molecular weight scaling exponents in a range where the size of the tracer, Rg, already considerably exceeds the gel pore size, g. IntroductionThe microscopic polymer mode coupling (PMC) theory connects the dynamics of entangled polymeric systems to the underlying equilibrium liquid structure. This description therefore naturally includes corrections arising from the finite molecular weights of tracer or matrix polymers. In the preceding paper, 1 referred to as paper I, the PMC predictions with finite size corrections have been worked out for the transport properties of entangled solutions and melts and for polymer tracer motion in gels. In the present paper these results are compared with data from many experiments. As the PMC approach has been detailed in the preceding paper, 1 it shall be summarized only shortly in this section and then compared to alternative approaches. The resulting formulas of paper I will be referenced by the equation numbers of that paper with a prefix I.The PMC approach of paper I treats the Rouseentangled crossover problem in a simple interpolative manner. The PMC contributions capturing the entanglement corrections are combined with the Rouse, unentangled quantities, see eqs I.52 and I.68 for D, eqs I.55 and I.67 for η, and eqs I.58 and I.70 for τ . Appreciable deviations from the asymptotes for high molecular weights are therefore not explained by corrections of the Rouse dynamics to the asymptotic, entangled motion. In stark contrast to the contour length fluctuation model of Doi, 2,3 the repton model of Rubinstein, 4 and the Rouse-fluc...

show abstract

Section: Rmentioning

confidence: 82%

Section: Discussionmentioning

confidence: 99%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Fuchs

Schweizer

1997

Macromolecules

View full text Add to dashboard Cite

show abstract

“…Especially, the long standing issue of the dependence of the shear viscosity on molecular weight should be mentioned; experimentally η ∼ M 3.4±0.2 is observed 1 , whereas both theories predict η ∼ M 3 asymptotically. Moreover, recent experiments on entangled polymer solutions [8][9][10] , and of the diffusion of polymer tracer chains in crosslinked gels 11,12 , find strong deviations from the theoretical predictions for the diffusion coefficients, D ∼ M −2 . Larger exponents, e.g.…”

Section: Introductionmentioning

confidence: 99%

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Fuchs

Schweizer

1997

Macromolecules

View full text Add to dashboard Cite

The transport coefficients of dense polymeric fluids are approximately calculated from the microscopic intermolecular forces. The following finite molecular weight effects are discussed within the Polymer-Mode-Coupling theory (PMC) and compared to the corresponding reptation/ tube ideas: constraint release mechanism, spatial inhomogeneity of the entanglement constraints, and tracer polymer shape fluctuations. The entanglement corrections to the single polymer Rouse dynamics are shown to depend on molecular weight via the ratio N/N e , where the entanglement degree of polymerization, N e , can be measured from the plateau shear modulus. Two microscopically defined non-universal parameters, an entanglement strength 1/α and a length scale ratio, δ = ξ ρ /b, where ξ ρ and b are the density screening and entanglement length respectively, are shown to determine the reduction of the entanglement effects relative to the reptation-like asymptotes of PMC theory. Large finite size effects are predicted for reduced degrees of polymerization up to N/N e ≤ 10 3 . Effective power law variations for intermediate N/N e of the viscosity, η ∼ N x , and the diffusion constant, D ∼ N −y , can be explained with exponents significantly exceeding the asymptotic, reptation-like values, x ≥ 3 and y ≥ 2, respectively. Extensions of the theory to treat tracer dielectric relaxation, and polymer transport in gels and other amorphous systems, are also presented.Macromolecules, accepted (May 1997).

show abstract

“…[33][34][35][36][37][38][39] The reasons behind the paucity of data concern the difficulty in finding an experimental technique capable of measuring ensemble-averaged, single segment, mean-squared displacements with the necessary coincidence of time and distance scales. Neutron scattering experiments 38 have provided access at distances below and just beyond the tube diameter, a, while NMR field gradient measurements have revealed anomalous diffusion just below the polymer end-to-end distance.…”

Section: Introductionmentioning

confidence: 99%

Segmental motion of entangled random coil polymers studied by pulsed gradient spin echo nuclear magnetic resonance

Komlosh

Callaghan

1998

The Journal of Chemical Physics

View full text Add to dashboard Cite

Pulsed gradient spin echo nuclear magnetic resonance ͑NMR͒ is used to investigate polymer mean-squared segmental displacements in semidilute solutions of high molar mass polystyrene in deuterio-toluene. Nine molar masses from 1 to 20 million daltons are studied at a fixed concentration of 5% w/v, and a range of concentrations from 5% to 20% at fixed molar mass of 3 million daltons. The distance and time scales accessed are 20 to 1000 nm and 10 to 3000 ms, respectively. Evidence for intrachain spin diffusion is found and its effect corrected for. The time dependence of mean-squared segmental displacements is fitted to the predictions of the Doi-Edwards model and tube disengagement times and tube diameters obtained.

show abstract

Self-diffusion and viscoelasticity of linear polystyrene in entangled solutions

Cited by 38 publications

References 10 publications

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 2. Comparison with Experiment

Polymer-Mode-Coupling Theory of Finite-Size-Fluctuation Effects in Entangled Solutions, Melts, and Gels. 1. General Formulation and Predictions

Segmental motion of entangled random coil polymers studied by pulsed gradient spin echo nuclear magnetic resonance

Contact Info

Product

Resources

About